Cause of Alpha or Black Artefacts in Render
The artifacts are not from z-fighting, but from transparent auto shadows bias.

Just turn the option off:


Shadow auto bias on:


Shadow auto bias off:






Elaboration:

There was once bug which was (supposedly) fixed for 2.68:


  Found the cause of the problem, it's due to the ray bias options that tries to avoid bad ray traced shadows.


It's supposed to eliminate shadow artifacts on smooth shaded surfaces where the shadow terminator is - like this one (I think..):



My guess is that blender sometimes fails to get it automatically right, setting it to fix value then works better.

Or making the surface flat shaded should work also.